Week 6 Homework
Score: $27.2 / 30 29 / 30$ answered
Question 18
区0/1 pt $5 ⇄ 95 C$
Constructing a Confidence Interval for a Population Mean
You intend to estimate a population mean $μ$ with the following sample.
$Unknown environment 'tabular'$
You believe the population is normally distributed. Find the $90 %$ confidence interval for the population mean. Enter your answer as an open-interval (i.e., parentheses) accurate to two decimal places.
$90 % c.1. =$
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$CI = (\overset{―}{x} - t^{*} \frac{s}{\sqrt{n}}, \overset{―}{x} + t^{*} \frac{s}{\sqrt{n}}) = (14 - 1.753 (0.6175), 14 + 1.753 (0.6175)) = (13.08, 14.92)$

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Step 1 ： $n = 16$

Step 2 ： $\overset{―}{x} = \frac{1}{16} (14 + 12 + 18 + 14 + 14 + 16 + 17 + 11 + 12 + 15 + 12 + 12) = 14$

Step 3 ： $s = \sqrt{\frac{1}{15} ((14 - 14)^{2} + (12 - 14)^{2} + (18 - 14)^{2} + (14 - 14)^{2} + (14 - 14)^{2} + (16 - 14)^{2} + (17 - 14)^{2} + (11 - 14)^{2} + (12 - 14)^{2} + (15 - 14)^{2} + (12 - 14)^{2} + (12 - 14)^{2})}$ = \sqrt{6.27} \)

Step 4 ： $\frac{s}{\sqrt{n}} = \frac{\sqrt{6.27}}{\sqrt{16}} = 0.6175$

Step 5 ： $t^{*} = 1.753$ (based on 90\% confidence level and $n - 1 = 15$ degrees of freedom)

Step 6 ： $CI = (\overset{―}{x} - t^{*} \frac{s}{\sqrt{n}}, \overset{―}{x} + t^{*} \frac{s}{\sqrt{n}}) = (14 - 1.753 (0.6175), 14 + 1.753 (0.6175)) = (13.08, 14.92)$

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